Your best bet for finding these fragments is to build a scanner room near the Mushroom Forest, equip a HUD chip, then set off in search of the fragments. Bridge fragments also spawn in the Mushroom Forest, in addition to the Sea Treader’s Path. The bridge is possibly the first component for which you will find fragments, as they can spawn near the Aurora crash zone. With the HUD chip equipped, you’ll have no problem finding the fragments assuming your scanner is in range to locate them. To make things easier, you should build a scanner room and search for components.
Each component will have fragments dotted about in various areas, so you’ll need to prepare for a bit of exploration.
The Cyclops is no different, requiring three scans of three different components before you can build the submersible. In Subnautica, you must scan fragments of damaged bits of machinery in order to unlock blueprints.